Importance Sampling via Variational Optimization

Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are extremely unlikely even alternative algorithms such as variational methods and stochastic sampling often perform poorly. We present a new importance sampling algorithm for Bayesian networks which is based on variational techniques. We use the updates of the importance function to predict whether the stochastic sampling converged above or below the true likelihood, and change the proposal distribution accordingly. The validity of the method and its contribution to convergence is demonstrated on hard networks of large genetic linkage analysis tasks.